Homeomorphisms of Bagpipes

Abstract

We investigate the mapping class group of an orientable $\omega$-bounded surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a bag (a compact surface with boundary) and finitely many long pipes. The subgroup consisting of classes of homeomorphisms fixing the boundary of the bag is a normal subgroup and is a homomorphic image of the product of mapping class groups of the bag and the pipes.